Yeah, it lags just like any other Samsung Galaxy series phones, but I have a AT&T version.
I have 4.4.2 NC2 Kitkat from AT&T. Did factory reset several times now and not rooted (there's no known root).
Waking up by pressing power button to see the time, half the time there's 2 second lag until screen turns on.
So now the phone is waken up. Open the dialer, it takes 1-3 seconds.
Open Contacts, it takes another 10-20 seconds because there's a ******* AT&T Address book popup with "Checking Subscriber Information" bull**** message. WTF. This probably has to do with my Note 3 being a AT&T crapped version.
Scrolling around the home screen or app list doesn't lag. Web browsing in Chrome doesn't lag (any worse than other mobile phones).